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Solyaev, Y. O.; Korolenko, V. A.

Application of Papkovich-Neuber general solution for crack problems in strain gradient elasticity. (English) Zbl 1525.74185

Lobachevskii J. Math. 44, No. 6, 2469-2479 (2023).
Summary: In this paper, we use the Papkovich-Neuber potentials to derive the variant of general solution for the plain problems of strain gradient elasticity theory (SGET) in bounded domains. General solution contains complete sets of functions satisfying 2D Laplace equations and modified Helmholtz equations, including the polynomial and modified Bessel functions of integer and fractional orders with corresponding angular periodicity. It is shown that proposed form of general solution allows to derive the known SGET asymptotic solutions for the crack-tip fields.

MSC:

74R10 Brittle fracture
74B99 Elastic materials
74G10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics
74G70 Stress concentrations, singularities in solid mechanics

Keywords:

Laplace equation; modified Helmholtz equation; series expansion; modified Bessel function; asymptotic plane-strain crack-tip field
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References:

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